Question

Help please !!!!!!!!!!!!!!!!!!

Answer 1

Answer:

n = 59

Step-by-step explanation:

There's definitely a better way, i just did math randomly but here goes:

First i squared both sides. which gets you:

$(\sqrt{n+5}-\sqrt{n-10} )(\sqrt{n+5}-\sqrt{n-10} )=1^2\\\\n+5 -2\sqrt{(n+5)(n-10)} +n-10=1$

Cleaning this up gives you:

$2n-5 -2\sqrt{(n+5)(n-10)}=1$

Now move everything to the other side so we can square this equation again

$-2\sqrt{(n+5)(n-10)}=-2n+6$

Divide both sides by -2

$\sqrt{(n+5)(n-10)}=n-3$

square again

$(n+5)(n-10)=(n-3)^2\\n^2-5n-50=n^2-6n+9$

subtract n^2 from both sides, add 6n, and add 50

$-5n-50=-6n+9\\n-50 = 9\\n=59$

Put this back into the equation and you get a correct answer!

sqrt(59 + 5) = sqrt(64) = 8

sqrt(59-10) = sqrt(49) = 7

8 - 7 = 1